Refactor bit iteration infrastructure:

* `to_bits` -> `to_bits_le`
* `BitIterator` -> `BitIteratorLE` + `BitIteratorBE`
* `found_one`/`seen_one` -> `BitIteratorBE::without_leading_zeros`

Author: Pratyush

algebra-core/src/biginteger/macros.rs

@@ -169,7 +169,7 @@ macro_rules! bigint_impl {
             #[inline]
             fn to_bits(&self) -> Vec<bool> {
                 let mut res = Vec::with_capacity(256);
-                for b in BitIterator::new(self.0) {
+                for b in BitIteratorBE::new(self.0) {
                     res.push(b);
                 }
                 res

algebra-core/src/biginteger/mod.rs

@@ -1,6 +1,6 @@
 use crate::{
     bytes::{FromBytes, ToBytes},
-    fields::BitIterator,
+    fields::BitIteratorBE,
     io::{Read, Result as IoResult, Write},
     CanonicalDeserialize, CanonicalSerialize, ConstantSerializedSize, SerializationError,
     UniformRand, Vec,

algebra-core/src/bytes.rs

@@ -152,12 +152,12 @@ macro_rules! to_bytes {
 macro_rules! push_to_vec {
     ($buf:expr, $y:expr, $($x:expr),*) => ({
         {
-            ToBytes::write(&$y, &mut $buf)
+            $crate::ToBytes::write(&$y, &mut $buf)
         }.and({$crate::push_to_vec!($buf, $($x),*)})
     });
 
     ($buf:expr, $x:expr) => ({
-        ToBytes::write(&$x, &mut $buf)
+        $crate::ToBytes::write(&$x, &mut $buf)
     })
 }
 
@@ -311,7 +311,6 @@ impl<T: FromBytes> FromBytes for Option<T> {
 
 #[cfg(test)]
 mod test {
-    use super::ToBytes;
     use crate::Vec;
     #[test]
     fn test_macro_empty() {

algebra-core/src/curves/mod.rs

@@ -180,17 +180,9 @@ pub trait ProjectiveCurve:
     /// Performs scalar multiplication of this element.
     fn mul<S: Into<<Self::ScalarField as PrimeField>::BigInt>>(mut self, other: S) -> Self {
         let mut res = Self::zero();
-
-        let mut found_one = false;
-
-        for i in crate::fields::BitIterator::new(other.into()) {
-            if found_one {
-                res.double_in_place();
-            } else {
-                found_one |= i;
-            }
-
-            if i {
+        for b in crate::fields::BitIteratorBE::without_leading_zeros(other.into()) {
+            res.double_in_place();
+            if b {
                 res += self;
             }
         }

algebra-core/src/curves/models/bls12/g2.rs

@@ -6,7 +6,7 @@ use crate::{
         short_weierstrass_jacobian::{GroupAffine, GroupProjective},
         AffineCurve,
     },
-    fields::{BitIterator, Field, Fp2},
+    fields::{BitIteratorBE, Field, Fp2},
     io::{Result as IoResult, Write},
     Vec,
 };
@@ -75,7 +75,7 @@ impl<P: Bls12Parameters> From<G2Affine<P>> for G2Prepared<P> {
             z: Fp2::one(),
         };
 
-        for i in BitIterator::new(P::X).skip(1) {
+        for i in BitIteratorBE::new(P::X).skip(1) {
             ell_coeffs.push(doubling_step::<P>(&mut r, &two_inv));
 
             if i {

algebra-core/src/curves/models/bls12/mod.rs

@@ -7,7 +7,7 @@ use crate::{
         fp12_2over3over2::{Fp12, Fp12Parameters},
         fp2::Fp2Parameters,
         fp6_3over2::Fp6Parameters,
-        BitIterator, Field, Fp2, PrimeField, SquareRootField,
+        BitIteratorBE, Field, Fp2, PrimeField, SquareRootField,
     },
 };
 use num_traits::One;
@@ -105,7 +105,7 @@ impl<P: Bls12Parameters> PairingEngine for Bls12<P> {
 
         let mut f = Self::Fqk::one();
 
-        for i in BitIterator::new(P::X).skip(1) {
+        for i in BitIteratorBE::new(P::X).skip(1) {
             f.square_in_place();
 
             for (p, ref mut coeffs) in &mut pairs {

algebra-core/src/curves/models/bw6/g2.rs

@@ -6,7 +6,7 @@ use crate::{
         short_weierstrass_jacobian::{GroupAffine, GroupProjective},
         AffineCurve,
     },
-    fields::{BitIterator, Field},
+    fields::{BitIteratorBE, Field},
     io::{Result as IoResult, Write},
     Vec,
 };
@@ -83,7 +83,7 @@ impl<P: BW6Parameters> From<G2Affine<P>> for G2Prepared<P> {
             z: P::Fp::one(),
         };
 
-        for i in BitIterator::new(P::ATE_LOOP_COUNT_1).skip(1) {
+        for i in BitIteratorBE::new(P::ATE_LOOP_COUNT_1).skip(1) {
             ell_coeffs_1.push(doubling_step::<P>(&mut r));
 
             if i {

algebra-core/src/curves/models/bw6/mod.rs

@@ -6,7 +6,7 @@ use crate::{
     fields::{
         fp3::Fp3Parameters,
         fp6_2over3::{Fp6, Fp6Parameters},
-        BitIterator, Field, PrimeField, SquareRootField,
+        BitIteratorBE, Field, PrimeField, SquareRootField,
     },
 };
 use num_traits::One;
@@ -238,7 +238,7 @@ impl<P: BW6Parameters> PairingEngine for BW6<P> {
         // f_{u+1,Q}(P)
         let mut f_1 = Self::Fqk::one();
 
-        for i in BitIterator::new(P::ATE_LOOP_COUNT_1).skip(1) {
+        for i in BitIteratorBE::new(P::ATE_LOOP_COUNT_1).skip(1) {
             f_1.square_in_place();
 
             for (p, ref mut coeffs) in &mut pairs_1 {

algebra-core/src/curves/models/mnt4/mod.rs

@@ -6,7 +6,7 @@ use crate::{
     fields::{
         fp2::{Fp2, Fp2Parameters},
         fp4::{Fp4, Fp4Parameters},
-        BitIterator, Field, PrimeField, SquareRootField,
+        BitIteratorBE, Field, PrimeField, SquareRootField,
     },
     One, Zero,
 };
@@ -111,18 +111,9 @@ impl<P: MNT4Parameters> MNT4<P> {
         let mut dbl_idx: usize = 0;
         let mut add_idx: usize = 0;
 
-        let mut found_one = false;
-
-        for bit in BitIterator::new(P::ATE_LOOP_COUNT) {
-            // code below gets executed for all bits (EXCEPT the MSB itself) of
-            // mnt6_param_p (skipping leading zeros) in MSB to LSB order
-            if !found_one && bit {
-                found_one = true;
-                continue;
-            } else if !found_one {
-                continue;
-            }
-
+        // code below gets executed for all bits (EXCEPT the MSB itself) of
+        // mnt6_param_p (skipping leading zeros) in MSB to LSB order
+        for bit in BitIteratorBE::without_leading_zeros(P::ATE_LOOP_COUNT).skip(1) {
             let dc = &q.double_coefficients[dbl_idx];
             dbl_idx += 1;
 

algebra-core/src/curves/models/mnt6/mod.rs

@@ -6,7 +6,7 @@ use crate::{
     fields::{
         fp3::{Fp3, Fp3Parameters},
         fp6_2over3::{Fp6, Fp6Parameters},
-        BitIterator, Field, PrimeField, SquareRootField,
+        BitIteratorBE, Field, PrimeField, SquareRootField,
     },
     One, Zero,
 };
@@ -113,18 +113,9 @@ impl<P: MNT6Parameters> MNT6<P> {
         let mut dbl_idx: usize = 0;
         let mut add_idx: usize = 0;
 
-        let mut found_one = false;
-
-        for bit in BitIterator::new(P::ATE_LOOP_COUNT) {
-            // code below gets executed for all bits (EXCEPT the MSB itself) of
-            // mnt6_param_p (skipping leading zeros) in MSB to LSB order
-            if !found_one && bit {
-                found_one = true;
-                continue;
-            } else if !found_one {
-                continue;
-            }
-
+        // code below gets executed for all bits (EXCEPT the MSB itself) of
+        // mnt6_param_p (skipping leading zeros) in MSB to LSB order
+        for bit in BitIteratorBE::without_leading_zeros(P::ATE_LOOP_COUNT).skip(1) {
             let dc = &q.double_coefficients[dbl_idx];
             dbl_idx += 1;